Traditionally, the angular momentum of light is calculated for "bullet-like" electromagnetic wave packets, although in actual optical experiments "pencil-like" beams of light are more commonly used. The fact that a wave packet is bounded transversely and longitudinally while a beam has, in principle, an infinite extent along the direction of propagation, renders incomplete the textbook calculation of the spin/orbital separation of the angular momentum of a light beam. In this work we demonstrate that a novel, extra surface part must be added in order to preserve the gauge invariance of the optical angular momentum per unit length. The impact of this extra term is quantified by means of two examples: a Laguerre-Gaussian and a Bessel beam, both circularly polarized.

14 pages, 1 figure